Moment-Tension Interaction Report
| Overall Verdict | PASS — 3/3 checks passed |
| Governing Check | Propagation |
| Governing Utilisation | 0.522 |
| Margin | 47.8% |
| Design Code | API RP 1111 |
| Pipe | OD 273.05 mm × WT 21.44 mm, X65 |
| Pressure | Pi = 20.00 MPa, Pe = 10.00 MPa (Pnet = 10.00 MPa) |
Independent of bending moment and tension — these set the baseline utilisation.
| Check | Capacity (MPa) | Design Factor | Allowable (MPa) | Demand (MPa) | Utilisation | Status |
|---|---|---|---|---|---|---|
| Burst Sec 4.3.1.1 | 75.26 | 0.72 | 54.19 | 10.00 | 0.185 | PASS |
| Collapse Sec 4.3.2 | 67.02 | 0.80 | 53.61 | 10.00 | 0.187 | PASS |
| Propagation Sec 4.3.3 | 23.96 | 0.80 | 19.17 | 10.00 | 0.522 | PASS |
Pure tension and pure bending limits at util = 1.0 for each API RP 1111 operating condition. Tension limits are asymmetric due to hoop stress interaction: positive tension (pipe stretching) is more favourable than compression when net internal pressure is positive.
| Condition | fd | T+ (kN) | T− (kN) | Mallow (kN·m) |
|---|---|---|---|---|
| Normal Operating | 0.72 | 5864.3 | -4954.6 | 289.2 |
| Installation | 0.80 | 6477.5 | -5567.8 | 325.1 |
| Extreme | 0.96 | 7700.9 | -6791.2 | 396.5 |
| Survival | 1.00 | 8006.3 | -7096.6 | 414.3 |
Capacity limits recomputed at baseline, +50%, and +100% internal pressure. Higher hoop stress shrinks all envelopes and increases the asymmetry between positive and negative tension limits.
| Pi (MPa) | σh (MPa) | Condition | fd | T+ (kN) | T− (kN) | Mallow (kN·m) |
|---|---|---|---|---|---|---|
| 20 | 53.7 | Normal Operating | 0.72 | 5864.3 | -4954.6 | 289.2 |
| Installation | 0.80 | 6477.5 | -5567.8 | 325.1 | ||
| Extreme | 0.96 | 7700.9 | -6791.2 | 396.5 | ||
| Survival | 1.00 | 8006.3 | -7096.6 | 414.3 | ||
| 30 (+50%) | 107.4 | Normal Operating | 0.72 | 6144.3 | -4324.8 | 252.5 |
| Installation | 0.80 | 6775.7 | -4956.3 | 289.4 | ||
| Extreme | 0.96 | 8026.1 | -6206.7 | 362.4 | ||
| Survival | 1.00 | 8336.8 | -6517.5 | 380.5 | ||
| 40 (+100%) | 161.0 | Normal Operating | 0.72 | 6293.8 | -3564.7 | 208.1 |
| Installation | 0.80 | 6959.8 | -4230.7 | 247.0 | ||
| Extreme | 0.96 | 8259.4 | -5530.3 | 322.9 | ||
| Survival | 1.00 | 8579.8 | -5850.7 | 341.6 |
The API RP 1111 combined check evaluates the Von Mises equivalent stress: σvm = √(σL² − σL·σh + σh²) ≤ fd·SMYS
The contour plot below maps utilisation across the bending moment vs. tension envelope. The bold black contour at util = 1.0 is the acceptance boundary; the dashed contour at 0.8 marks a typical design target.
Each curve traces the maximum allowable bending moment as a function of applied tension, at util = 1.0 for that operating condition. The Normal Operating envelope (innermost) is the most conservative; the Survival envelope (outermost) represents the full yield limit.
| Tension (kN) | Normal Operating Mallow (kN·m) | Installation Mallow (kN·m) | Extreme Mallow (kN·m) | Survival Mallow (kN·m) |
|---|---|---|---|---|
| -4955 | 0.0 | 0.0 | 0.0 | 0.0 |
| -4414 | 31.6 | 35.2 | 42.3 | 44.1 |
| -3873 | 63.1 | 70.4 | 84.6 | 88.2 |
| -3332 | 94.8 | 105.5 | 126.9 | 132.3 |
| -2791 | 126.3 | 140.7 | 169.2 | 176.3 |
| -2250 | 157.9 | 175.8 | 211.5 | 220.4 |
| -1709 | 189.5 | 211.0 | 253.8 | 264.6 |
| -1168 | 221.1 | 246.1 | 296.1 | 308.6 |
| -627 | 252.7 | 281.3 | 338.4 | 352.7 |
| -86 | 284.2 | 316.5 | 380.8 | 396.8 |
| 455 | 315.8 | 351.6 | 423.1 | 440.9 |
| 996 | 284.2 | 316.5 | 380.8 | 396.8 |
| 1537 | 252.7 | 281.3 | 338.4 | 352.7 |
| 2078 | 221.1 | 246.1 | 296.1 | 308.6 |
| 2619 | 189.5 | 211.0 | 253.8 | 264.6 |
| 3160 | 157.9 | 175.8 | 211.5 | 220.4 |
| 3701 | 126.3 | 140.7 | 169.2 | 176.3 |
| 4241 | 94.8 | 105.5 | 126.9 | 132.3 |
| 4782 | 63.1 | 70.4 | 84.6 | 88.2 |
| 5323 | 31.6 | 35.2 | 42.3 | 44.1 |
| 5864 | 0.0 | 0.0 | 0.0 | 0.0 |
Utilisation at selected engineering reference points on the M–T plane.
| Point | T (kN) | M (kN·m) | T / Ty | M / Mp | Utilisation | Margin | Status |
|---|---|---|---|---|---|---|---|
| Pressure only (origin) | 0.0 | 0.0 | 0.000 | 0.000 | 0.166 | 83.4% | PASS |
| T = 0.5 T_y | 3796.2 | 0.0 | 0.500 | 0.000 | 0.628 | 37.2% | PASS |
| T = 0.8 T_y | 6073.9 | 0.0 | 0.800 | 0.000 | 1.038 | 0.0% | FAIL |
| T = 1.0 T_y | 7592.4 | 0.0 | 1.000 | 0.000 | 1.314 | 0.0% | FAIL |
| M = 0.5 M_p | 0.0 | 304.8 | 0.000 | 0.500 | 1.048 | 0.0% | FAIL |
| M = 0.8 M_p | 0.0 | 487.6 | 0.000 | 0.800 | 1.618 | 0.0% | FAIL |
| M = 1.0 M_p | 0.0 | 609.5 | 0.000 | 1.000 | 1.998 | 0.0% | FAIL |
| T = 0.5 T_y + M = 0.5 M_p | 3796.2 | 304.8 | 0.500 | 0.500 | 1.573 | 0.0% | FAIL |
| T = 0.5 T_y + M = 0.8 M_p | 3796.2 | 487.6 | 0.500 | 0.800 | 2.144 | 0.0% | FAIL |
| T = 0.8 T_y + M = 0.5 M_p | 6073.9 | 304.8 | 0.800 | 0.500 | 1.988 | 0.0% | FAIL |
| Outer Diameter (OD) | 273.05 mm |
| Wall Thickness (WT) | 21.44 mm |
| Inner Diameter (ID) | 230.17 mm |
| D/t Ratio | 12.7 |
| Corrosion Allowance | 1.00 mm |
| Grade | X65 |
| SMYS | 448.00 MPa |
| SMTS | 531.00 MPa |
| Young’s Modulus | 207 GPa |
| Poisson’s Ratio | 0.30 |
| Fabrication Type | Seamless |
| Internal Pressure (Pi) | 20.00 MPa |
| External Pressure (Pe) | 10.00 MPa |
| Net Pressure (Pnet) | 10.00 MPa |
| Hoop Stress (σh) | 53.68 MPa |
| Cross-sectional Area (A) | 169.47 cm² |
| Section Modulus (Z) | 989.46 cm³ |
| Second Moment of Area (I) | 13508.60 cm⁴ |
| Yield Tension (Ty) | 7592.4 kN |
| Plastic Moment (Mp) | 609.5 kN·m |